I was told that abbreviations consist of initialisms (FBI), acronyms (NATO, a.k.a.), and shortened words (ad, bike).

But what about i.e. and e.g.? At the first glance, they look as initialisms, but typically we pronounce them as "for example" and "that is", not literally, like "eye ee".

So which subclass of abbreviations they belong to? Initialisms or maybe something different, and why? Are there reputable sources to classify them?